Phase transitions in Pareto optimal complex networks

The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem finding phase transitions of different kinds. Distinct phases are associated to different arrangements of the connections; but the need of drastic topological changes does not determine the presence, nor the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.Comment: 14 pages, 7 figure

Ascent trajectory optimisation for a single-stage-to-orbit vehicle with hybrid propulsion

This paper addresses the design of ascent trajectories for a hybrid-engine, high performance, unmanned, single-stage-to-orbit vehicle for payload deployment into low Earth orbit. A hybrid optimisation technique that couples a population-based, stochastic algorithm with a deterministic, gradient-based technique is used to maximize the nal vehicle mass in low Earth orbit after accounting for operational constraints on the dynamic pressure, Mach number and maximum axial and normal accelerations. The control search space is first explored by the population-based algorithm, which uses a single shooting method to evaluate the performance of candidate solutions. The resultant optimal control law and corresponding trajectory are then further refined by a direct collocation method based on finite elements in time. Two distinct operational phases, one using an air-breathing propulsion mode and the second using rocket propulsion, are considered. The presence of uncertainties in the atmospheric and vehicle aerodynamic models are considered in order to quantify their effect on the performance of the vehicle. Firstly, the deterministic optimal control law is re-integrated after introducing uncertainties into the models. The proximity of the final solutions to the target states are analysed statistically. A second analysis is then performed, aimed at determining the best performance of the vehicle when these uncertainties are included directly in the optimisation. The statistical analysis of the results obtained are summarized by an expectancy curve which represents the probable vehicle performance as a function of the uncertain system parameters. This analysis can be used during the preliminary phase of design to yield valuable insights into the robustness of the performance of the vehicle to uncertainties in the specification of its parameters

Gravity Effects on Information Filtering and Network Evolving

In this paper, based on the gravity principle of classical physics, we propose a tunable gravity-based model, which considers tag usage pattern to weigh both the mass and distance of network nodes. We then apply this model in solving the problems of information filtering and network evolving. Experimental results on two real-world data sets, \emph{Del.icio.us} and \emph{MovieLens}, show that it can not only enhance the algorithmic performance, but can also better characterize the properties of real networks. This work may shed some light on the in-depth understanding of the effect of gravity model